In each of these fallacies, the argument relies on premises that are not logically relevant to the conclusion. Such faulty arguments cannot be valid because, the premise is not relevant to the conclusion.

Argument from ignorance (from Latin: argumentum ad ignorantiamis) asserts that a proposition is true because it has not yet been proven false or that it is false because it has not yet been proven true.

Other names for this fallacy include: appeal to ignorance (in which ignorance represents “a lack of contrary evidence”).

Argument from ignorance is a fallacy because in the first case p can be false even if evidence against p has not yet been presented. For example it is a fallacy to argue that unless you can prove there are no unicorns, we will conclude unicorns exist. In another, somewhat more consequential example, unless you can prove your innocence, we will assume you are guilty. In the reverse case, lack of evidence is not evidence of absence. For example, it has always been true that the earth is round, even if conclusive evidence for its spherical shape had to wait for ocean exploration to advance. Also, although you cannot see germs, germs do exist and the germ theory of disease is well proven.

The Space Shuttle Challenger was declared safe to launch because the engineers could not prove it was unsafe.

This fallacy along with a misplaced burden of proof played a tragic role in the decision to launch the Space Shuttle Challenger on January 28, 1986. Engineers stated that they did not have enough data to ensure a safe launch during the unusually cold temperatures. This lack of evidence ensuring a failure was taken as evidence that it was safe to launch. The challenger broke apart 73 seconds into its flight, leading to the deaths of its seven crew members.

The precautionary principle seeks to avoid the argument from ignorance fallacy. The states that if an action or policy has a suspected risk of causing harm to the public, or to the environment, in the absence of scientific consensus (that the action or policy is not harmful), the burden of proof that it is not harmful falls on those taking an action that may or may not be a risk.

Understanding the role that evidence of absence plays in proving a claim is helpful in better understanding arguments from ignorance. It is true that “absence of evidence is not proof of absence”, however if diligent searches find no evidence, then this provides evidence of absence, commensurate with the thoroughness of the searchs. For example, many thorough searches have yet to provide any evidence for the existence of the Loch Ness Monster. Because these searches have been thorough, they provide significant evidence, but not proof, that the Loch Ness Monster does not exist.

The appeal to an inappropriate authority is a fallacy when the authority cited is not an expert in the topic at hand. It is important to make a distinction here between an expert and an authority. An expert has carefully examined representative evidence relevant to topics within his or her areas of expertise. For example, expert biologists are qualified, based on their knowledge, experience, training, or general circumstances, to offer an informed decision or opinion regarding topics with their domain of expertise. Appealing to their opinions on topics outside of their area of expertise is a fallacy, regardless of their stature, notoriety, charisma, or positional authority.

When we argue that a given conclusion is correct on the ground that an expert authority has come to that judgement, we commit no fallacy. In contrast, however, the argument ad verecundiam is an appeal to one who has no claim greater than our own to judge the truth of a proposition.[4]

The fallacy of appeal to an inappropriate authority often occurs when we are influenced by a celebrity endorsement of a product they have not expertise with. In an advertising campaign, actor Peter Bergman notoriously told the audience: “I’m not a doctor, but I play one on TV” in an attempt to persuade the audience to choose Vicks Formula 44 to treat their cold symptoms. It is clearly a fallacy to take medical advice from an actor paid to promote a product. When a famous athlete endorses a particular automobile, soft drink, jewelry, or home appliance there is no valid reason to conclude they are sharing any expert opinion. Similarly, marriage advice from a celibate religious leader, science advice from an elected official, or political advice from a Nobel winning physicist carries no more weight than your own opinion in these matters.

In many cases, arguments from authority will be sound arguments. For example, when a person goes to a skilled doctor and the doctor tells him that he has a cold, then the patient has good reason to accept the doctor's conclusion. As another example, if a person's computer is acting odd and his friend, who is a computer expert, tells him it is probably his hard drive then he has good reason to believe her.[5]

Here is a useful checklist for taking advice and making decisions while avoiding appeal to an inappropriate authority:[6]

Is this a matter which I can decide without appeal to expert opinion? If the answer is "yes", then do so. If "no", go to the next question:

Is this a matter upon which expert opinion is available? If not, then your opinion will be as good as anyone else's. If so, proceed to the next question:

Is the authority an expert on the matter? If not, then why listen? If so, go on:

Is the authority biased towards one side? If so, the authority may be untrustworthy. At the very least, before accepting the authority's word seek a second, unbiased opinion. That is, go to the last question:

Is the authority's opinion representative of expert opinion? If not, then find out what the expert consensus is and rely on that. If so, then you may rationally rely upon the authority's opinion.

If an argument to authority cannot pass these five tests, then it commits the fallacy of appeal to inappropriate authority.

Several appeals to inappropriate authority bolstered support for military action in the lead up to the 2003 invasion of Iraq.

It can be dangerous to mistake the allure of authority for true expertise. Several appeals to inappropriate authority bolstered support for military action in the lead up to the 2003 invasion of Iraq. Several statements made by an informant known as Curveball were mistaken for expert advice. This led to false statements by President Bush in the 2003 state of the union address, and falsehoods in Colin Powell's presentation to the UN Security Council regarding mobile biological weapons laboratories. In a separate, but related incident mistaking forged documents for relevant authority regarding the Nigerian purchase of uranium, the governments of the United States and the United Kingdom asserted that Iraq violated United Nations Iraq sanctions by attempting to procure nuclear material for the purpose of creating weapons of mass destruction.

Ad hominem (Latin for "to the man" or "to the person”), short for argumentum ad hominem, is a logical fallacy in which an argument is rebutted by attacking the character, motive, or other attribute of the person making the argument, or persons associated with the argument, rather than attacking the substance of the argument itself.

Ad Hominem is a fallacy because the character, circumstances, or actions of a person do not (in most cases) have a bearing on the truth or falsity of the claim being made (or the quality of the argument being made).

A debater commits the Ad Hominem Fallacy when he or she introduces irrelevant personal premises about his or her opponent. Such red herrings may successfully distract the opponent or the audience from the topic of the debate.[8]

The major difficulty with labeling an element of reasoning an Ad Hominem fallacy is deciding whether the personal attack is relevant or irrelevant to the argument being made. For example, attacks on a person for their immoral sexual conduct are irrelevant to the quality of their mathematical reasoning, but they are relevant to arguments promoting the person for a leadership role requiring moral authority.[9]

President Barack Obama’s race is irrelevant to his policy positions or executive decisions. Donald Trump’s hair style is irrelevant to his campaign promises or suitability as a presidential candidate. To suggest otherwise and exploit latent prejudices against African Americans or hair styles is an Ad Hominem attack. By contrast, however, character is important and relevant to leadership performance. Therefore investigating allegations of President Bill Clinton’s infidelity and irregularities in George W. Bush’s military service record are relevant. These investigations are valid inquiries and are not Ad Hominem attacks.

Appeal to emotion or argumentum ad passiones is a logical fallacy characterized by the manipulation of the recipient's emotions in order to win an argument, especially in the absence of factual evidence.

This fallacy is committed when someone manipulates another’s emotions to get them to accept a claim as being true. More formally, this sort of fallacious reasoning involves the substitution of various means of producing strong emotions in place of evidence for a claim. If the favorable emotions associated with X influence the person to accept X as true because they "feel good about X," then he has fallen prey to the fallacy.

This sort of fallacious reasoning is very common in politics and it serves as the basis for a large portion of modern advertising. Most political speeches are aimed at generating feelings in people so that these feelings will get them to vote or act a certain way. In the case of advertising, the commercials are aimed at evoking emotions that will influence people to buy certain products. In most cases, such speeches and commercials are notoriously free of real evidence.

This sort of influence is quite evidently fallacious. It is fallacious because using various tactics to incite emotions in people does not serve as evidence for a claim. For example, if a person were able to inspire in someone an incredible hatred of the claim that 1+1 = 2 and then inspired the person to love the claim that 1+1 = 3, it would hardly follow that the claim that 1+1 = 3 would be adequately supported.[11]

One distinction between relevant and fallacious appeals to emotion is based on the distinction between arguments which aim to motivate us to action, and those which are intended to convince us to believe something. Appeals to emotion are always fallacious when intended to influence our beliefs, but they are sometimes reasonable when they aim to motivate us to act. The fact that we desire something to be true gives not the slightest reason to believe it, and the fact that we fear something being true is no reason to think it false; but the desire for something is often a good reason to pursue it, and fear of something else a good reason to flee.[12]

One example of this is that while it may feel better to believe global warming is a hoax, to do so simply because it gives positive emotions would be illogical.

The Daisy Advertisement used during the 1964 United States Presidential election is an example of using fear in an emotional appeal. The controversial advertisement shows a three year old girl standing in a meadow with chirping birds, picking the petals of a daisy and then cuts to a missile launch and a nuclear explosion. The advertisement relied on fear of a nuclear war to argue that voting to reelect President Johnson was a safer choice than voting for Barry Goldwater in the 1964 United States Presidential election. The argument is fallacious because there was no evidence that Goldwater was inclined to start a nuclear war.

The speeches of Adolph Hitler are often cited as examples of fallacious appeals to emotion. His speeches were persuasive and it did not turn out well.

An appeal to pity (also called argumentum ad misericordiam, or the sob story) is a fallacy in which someone tries to win support for an argument or idea by exploiting his or her opponent's feelings of pity or guilt. It is a specific kind of appeal to emotion in which the altruism and mercy of the audience are the special emotions appealed to.[13]

P is presented, with the intent to create pity.
Therefore claim C is true.

The fallacy is that pity does not serve as evidence for the claim. For example, a defense attorney may argue: “Ladies and gentlemen of the jury, look at this miserable man, in a wheelchair, unable to use his legs. Could such a man really be guilty of embezzlement?”

To discourage use of appeals to pity in the court room, under Rule 403 of the US Federal Rules of Evidence, evidence may be excluded if its probative value—relevance in determining guilt or innocence—is substantially outweighed by unfair prejudice. When applying this rule, the judge must consider the extent to which information unfairly arouses the emotions of the jury. Emotionalism is unfair if it is not connected to the facts of the case. For example, evidence of child abuse is always emotional, but whether it is unfairly emotional depends on the case. If the defendant is charged with burglary, getting the jury all riled up about child abuse is unfair, but if the defendant is charged with child abuse, the emotionalism is inherent in the case itself, and is "fair" prejudice.[15]

Appeal to force also known as Argumentum ad baculum (Latin for "argument to the cudgel" or "appeal to the stick"), is an argument where force, coercion, or the threat of force, is given as a justification.

The fallacy takes on the following form:

Claim that P is true, or suffer the consequences.

Galileo's initial discoveries were met with opposition within the Catholic Church, and in 1616 the Inquisition declared heliocentrism to be formally heretical. Heliocentric books were banned and Galileo was ordered to refrain from holding, teaching or defending heliocentric ideas.

abstain completely from teaching or defending this doctrine and opinion or from discussing it... to abandon completely... the opinion that the sun stands still at the center of the world and the earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing.

With no attractive alternatives Galileo accepted the orders delivered and through this invalid appeal to force the earth remained at the center of the universe.

The fallacy is still influential in more modern forms. Food libel laws are laws passed in thirteen U.S. states that make it easier for food producers to sue their critics for libel. In 1998, television talk-show host Oprah Winfrey and one of her guests, Howard Lyman, were involved in a lawsuit, surrounding the Texas version of a food libel law known as the False Disparagement of Perishable Food Products Act of 1995. Although the jury in the case found that the statements by Winfrey and Lyman did not constitute libel against the cattlemen, Winfrey no longer speaks publicly on the issue, going so far as to decline to make videotapes of the original interview available to enquiring journalists. This appeal to force has a chilling effect and silences critics of the food industry.

Irrelevant conclusion also known as Ignoratio elenchi, is the informal fallacy of presenting an argument that may or may not be logically valid, but fails nonetheless to address the issue in question. More colloquially, it is also known as missing the point.

The fallacy takes on the following form:

P therefore q

It is a fallacy because the truth value of p is not relevant to the truth value of q. The conclusion drawn is irrelevant to the premise.

The key in evaluating an argument is determining whether or not the appeal used in the argument is relevant to the conclusion or not. Relevance is established by either logical or evidential connection. One quick way to establish relevance is to ask yourself if the premises were false, would that fact imply that the conclusion is false also? If it would not, then the premises can be considered irrelevant to the conclusion.[16]

"We need the strongest military on the face of the planet, and everyone has to know it. And, specifically, what that means is we need about 50 Army brigades, we need about 36 Marine battalions, we need somewhere between 300 and 350 naval ships, we need to upgrade every leg of the nuclear triad…"[17]

This statement is a fallacy. The US already has the strongest military on the face of the planet by far, so no additional military buildup is required to become the strongest. Also, the major threats facing the US are terror threats by non-state actors. The buildup of conventional weapons she advocated here does not address the prevailing threat.